Andy: We might do business on a board, but I want to carve the pieces myself. One side in alabaster, the opposing side in soapstone. What do you think?
Red: I think it’ll take years.

Monday, November 12, 2007

Endgame Obsession #2 RaPvB

I became interested in this ending while watching the last game to finish from the 2005 Western States Open. Then-IM (now GM) Jesse Kraai was pressing against GM Alexander Stripunsky. A large crowd of about a hundred players were watching the game, aided by a demo board. I whispered to a 2300 player sitting near me, "Is there a win?" He nodded without elaborating. IM John Donaldson walked by and I heard him say, "It doesn't look like he knows the method." The way he said "method" got me hooked. There's a METHOD? What METHOD? The game ended with Kraai being unable to find the method over the board, running out of time, and conceding a draw. Eventually, I investigated this myself and found a complicated ending equal to my tendency to obsess. White must not advance the Pawn too quickly because Black can successfully blockade it at a6 under many circumstances. The White King ends up having to use a vacant a5 square in the winning method. Also note that if the pawn were gone, Black's King is in the proper corner to stalemate itself in a Rook versus Bishop drawn endgame.

(16) Kraai,J (2497) - Stripunsky,A (2629) [D13]

Western States Open Reno, NV (6.4), 16.10.2005

1.Nf3 d5 2.c4 c6 3.cxd5 cxd5 4.d4 Nc6 5.Nc3 Nf6 6.Bf4 Nh5 7.Bd2 g6 8.Qb3 e6 9.e3 Bg7 10.Be2 0-0 11.0-0 b6 12.Rfc1 Bb7 13.a4 Rb8 14.Rc2 Nf6 15.Rac1 Ne4 16.Be1 Nd6 17.Nb5 Rc8 18.Ne5 Nxe5 19.Nxd6 Qxd6 20.Bb4 Qb8 21.Bxf8 Rxf8 22.dxe5 Bxe5 23.h3 Rd8 24.Bb5 d4 25.exd4 Bxd4 26.Bc6 Bxc6 27.Rxc6 Qf4 28.Qf3 Qxf3 29.gxf3 Bxb2 30.Rc8 Rxc8 31.Rxc8+ Kg7 32.Rc7 a5 33.f4 Ba3 34.Kg2 Bd6 35.Rb7 Bc5 36.Kg3 h6 37.h4 Kf6 38.Kf3 Bd4 39.Rd7 e5 40.fxe5+ Bxe5 41.Ke4 h5 42.Rb7 Bc3 43.Rxb6+ Ke7 44.f4 Kf8 45.f5 Kg7 46.Ra6 f6 47.Ra7+ Kh6 48.Rf7 Be5 49.Rf8 Kg7 50.Ra8 Bc3 51.Rb8 Be1 52.Rb5 Kh6 53.Kf3 gxf5 54.Ke2 Bb4 55.Rxf5 Kg6 56.Rf1 Be7 57.Kd3 f5 58.Rh1 Bc5 59.Rc1 Bf2 60.Rc6+ Kf7 61.Ra6 Bxh4 62.Rxa5 Ke6 63.Ra6+ Kd7 64.Rh6 Kc7 65.Rxh5 Bg3 66.Rxf5+- Kb7 67.Rf6 Ka8 68.Rf7 I chose to deviate here from the game continuation in order to place the Bishop on its best diagonal, g1-a7. 68...Bh2 [ The actual game continued 68...Be5 69.Kc4 Bd6 70.Kb5 Be5 71.Ka6 Bg3 72.Ra7+ ( 72.a5 See method 2B below 72...Kb8 ( 72...Be5 73.Rf8+ Bb8 74.Kb5 Kb7 75.a6+ Ka8 76.Rg8 Ka7 77.Rg7+ Ka8 78.Kb6 Be5 79.Rd7 Bf4 80.a7 Be3+ 81.Ka6 Bb6 82.Re7 Bd8 83.Rg7 Bc7 84.Rg8+ Bb8 85.Rxb8#) 73.Kb6) 72...Kb8 73.Rg7 Bf2 74.Rg8+ Kc7 75.Rg2 Bd4 76.Rg4 Be3 77.Rb4 Kc8 78.Rb5 Kc7 79.Rb1 Kc8 80.Rb7 Bf2 81.Rb5 Kc7 82.Rb1 Be3 83.Rb2 Kc8 84.Rb3 Bf2 85.Rb5 Kc7 Draw eventually agreed after a time scramble.] 69.Kc4 Bg1 Black's best defense involves keeping his king out of checkmate threats, e.g. when White has his king on the a-file, his own king is on the c-file and vice versa. The Bishop is best placed on the g1-a7 diagonal to prevent White's usage of Kb6 and eventually to stop an advancing Pa7. SETUP: White aims for Ka6 and then Rb7+ to force Black to choose his last stand at a8 or c8.70.Kb5 Bd4 71.Ka6 Kb8 72.Rb7+ Setup complete. Black's main resource in this ending is that the a-pawn can either be blocked by the Black King or the White King. When the White King goes to a6, the Black King's best defense is to go to c8. When the White King crosses to the c-file, the Black King does well to cross over to the a-file. If Black allows White to press the vertical opposition mate threats will appear. White's strategy consists of three plans: OPERATION CROSS OVER: moving the White King from the a-file to the c-file without allowing the Black King to cross over to the a-file. This typically involves a maneuver such as Ka6-a5-b4. OPERATION CUT OFF: pushing the Black King to the d-file and cutting him off with the White Rook on the c-file, perhaps with lateral opposition from the White King on the a-file. This usually happens when the Black King moves to c6. And OPERATION PUSH PAWN: If the Black Bishop can be prevented from getting onto the g1-a7 diagonal for a while, White uses both the Rook and the King to escort the pawn to a7. This typically happens when the Bishop goes to the edge of the board. When the pawn reaches a7, the Bishop must not be allowed to sacrifice itself for stalemate.

PLAN B [ 72...Ka8 PLAN B, PHASE 1: White's job is a little easier in this variation. The overall plan is to advance the a-pawn to a7 while threatening mate on the back rank, ultimately winning a pinned bishop at b8. The position of the kings facing each other in the corner and the pawn on the 4th are important to MEMORIZE with the rook anywhere safe on the seventh and the bishop anywhere on the g1-a7 diagonal. This is the moment for PHASE 1: Advance The Pawn to the 5th. 73.a5! Bf2 PLAN B, PHASE 2: Force the bishop to b8. 74.Rf7 Bc5! This move offers a bit more resistance because Rc7 is a little too close to the King to carry through all the mate threats. Nevertheless, wherever the bishop goes, the rook travels laterally to hit it and threaten checkmate. The goal is to pin the bishop at b8 from a kingside square e8-h8. ( 74...Bg3 75.Kb6 Bh2 76.Rg7 Be5 77.Ra7+ Kb8 78.Rd7) 75.Rc7 Bd6 This is the only move that prevents mate. Notice that from d6, the Bishop does not have enough checking distance to deter a White King at b6. 76.Rg7 This square and the e7 square are good spots for the White Rook because they are far away from the Black King and they threatens to move to eighth rank squares which cannot be controlled by the Black Bishop. 76...Bb8 ( 76...Kb8 77.Kb6!; 76...Be5 77.Rg8+ Bb8 78.Kb5!) 77.Re7 The Rook MUST arrive on the eighth rank with check. 77...Bd6 78.Re8+ Bb8 79.Kb5! This stalemate-avoiding move is one that White must remember. Again Black has two paths, but they soon converge. PLAN B, PHASE 3: Use waiting moves (Re8 or Rg8) to get the Black King to come out on the 7th, check it back with the rook (Re7+ or Rg7+) and then advance Pa6. Use a similar maneuver to get the King on b6. Beware of stalemate always. 79...Kb7 ( 79...Ka7 80.Re7+ Ka8 81.a6 transposes to the 79...Kb7 line.) 80.Re7+ ( 80.a6+ also works. 80...Ka8 81.Rg8 Ka7 82.Rg7+ Ka8 83.Kb6) 80...Ka8 ( 80...Kc8 81.a6 Kd8 82.a7+-) 81.a6 Ba7 82.Re8+ Bb8 83.Rg8 Ka7 84.Rg7+ Ka8 85.Kb6 Be5 86.Rd7 guarding against Bishop check from d4. 86...Bg3 87.a7 Bf2+ 88.Ka6 Bb6 Watch out for stalemate! 89.Rg7 Bd8 Watch out for stalemate! The Rook MUST arrive on the eighth with check. 90.Rg6 Bf6 Watch out for stalemate! 91.Rg8+ Bd8 92.Rxd8#]

PLAN A: 72...Kc8 The tablebase shows that not only does this resist six moves longer, but it is also quite a bit more complicated than Ka8. PLAN A, PHASE 1: Set up OPERATION CROSS OVER: getting the White King to the c-file without allowing the Black King to get back to the a-file. 73.Rb5 With the Black King on c8, White starts by setting up Operation Cross Over with two paths. If Black commits to a Bishop move, White tries for the two branches of the Cross Over beginning with Ka5. If Black plays Kc7, then the Rook has to play to Rb3 to set up a king feint at Ka5-b4-c4.73...Kc7 This resists more stubbornly than Bishop moves. PLAN A, PHASE 2: If the Black King comes to c7, place the White Rook at g3, hitting the Bishop first if it's on f2. With the Black King cutting off one of the Cross Over pathways through b6, White has to do some dancing with the Rook against the Bishop. [ 73...Be3 74.Ka5 Bd2+ ( If Black doesn't prevent Operation Cross Over, then the win becomes fairly easy. 74...Kc7 75.Kb4 Bb6 76.a5 Ba7 77.a6 Bb6 Even if Black establishes the blockade of b6, as long as the White Rook stays on the b-file, the Black King cannot make it back to the a-file. 78.Kc4 Kc6 79.Rb1 Kc7 ( 79...Be3 80.Rb7 Bb6 81.Rh7 Be3 82.a7+-) 80.Kd5 Black would have a draw if his king were on a7 right now. 80...Be3 81.Rb7+ Kc8 82.Kc6 Bd4 83.a7+-) 75.Kb6 Kb8 76.Re5 guarding against Be3+ while threatening Re8#. 76...Kc8 77.a5 ( 77.Re8+ Kd7 78.Re4 Bg5 79.Rc4 Bd8+ 80.Kb5) 77...Bf4] 74.Rb3 If the Bishop is on d4, e3, or g1, put the rook on b3. If the Bishop is on f2, flush it to another square by moving Rb2 before moving Rb3. 74...Bf2 [ 74...Kc6? Black shouldn't volunteer for horizontal opposition because White then can start Operation Cut Off. The Rook chases the Bishop in order to quickly get to the c-file. 75.Rd3 Bf6 76.Rd2 Kc7 ( 76...Kc5 77.a5 Kb4 78.Rd5 should be an easy win.) 77.Ka7 Kc6 78.Rc2+ should be an easy win.; 74...Kc8] 75.Ka5 Here, the path diverges in several directions. If the Bishop goes to a7 or g1, White responds with Rb5 and tunneling his King through b4. If the Black King comes forward again, White plays Rb5. 75...Be1+ This causes a fumbled Operation Cross Over where Black's King jumps back to the opposite side. However, the Bishop becomes trapped in a sense such that it cannot get back to the g1-a7 diagonal for the next eight moves. [ 75...Bg1?! 76.Rb5 Be3 77.Kb4 achieves Operation Cross Over.; 75...Bd4?! 76.Kb4 Kb6?? 77.Kc4+ This discovery wins the Bishop.; 75...Kc8 76.Rb5 Ba7 ( 76...Be1+ 77.Kb6 Kb8 78.Rf5 guarding against the check on f2. 78...Kc8 79.Rf8+ Kd7 80.a5 Bb4 81.Rb8 Bd6 82.Rb7+ Ke6 83.a6+-) ; 75...Ba7 76.Rb5 Bd4 77.Kb4 achieves Operation Cross Over.; 75...Kc6 76.Rb5 This looks like White is just repeating moves, but now that Black has come forward, he is vulnerable to Operation Cut Off. 76...Bc5 Stops Kb4, Operation Cross Over. However, the Black King is stuck at c6 for a couple moves, allowing White to switch to Operation Cut Off. a) 76...Be1+ 77.Ka6 Kc7 78.Rb7+! While the Bishop is on the lame e1-a5 diagonal, White can make maneuvers such as Ka6-b6-c6. 78...Kc6 (a) 78...Kc8 79.Kb6! Ba5+ 80.Kc6 achieves Operation Cross Over.) 79.Rb1 Bd2 80.Rb2 Be1 81.Rc2+ achieves Operation Cut Off.; b) 76...Kc7 77.Kb4; 77.Ka6 taking the lateral opposition. 77...Be3 78.Rb3 Bd4 ( 78...Bd2 79.Rb2 Be1 80.Rc2+ achieves Operation Cut Off.) 79.Rd3 Bg7 ( 79...Bf6 80.Rd2 Kc7 81.Ka7!) 80.Rd2 Kc7 81.Ka7 Kc6 82.Rc2+ achieves Operation Cut Off.] 76.Kb5 Kb7 77.Rf3! The Rook at f3 controls so many squares that the Black Bishop requires at least four moves to get back to the g1-a7 diagonal. Meanwhile, White will try to push the a-pawn to a7.77...Bd2 78.a5 Bh6 79.a6+ Here the path diverges when Black chooses a8 or b8. If Ka8, then the next move is Kb6. If Bg7, then the response is Rh3. After either line, White's plan is basically Rd3, Rd7, Kb6, and a7. 79...Kb8! This route has a couple devious stalemate traps. White basically moves over to h3 to tag the Bishop before returning to the route Rd3-Rd7. [ 79...Ka8 White basically moves Kb6, followed by Rd3-d7 80.Kb6 Bg7 81.Rd3! denying the Bishop its d4 destination for at least another three moves. 81...Bf6 ( 81...Be5 82.Rd7) 82.Rd7 Bg5 83.a7 Be3+ 84.Ka6 Bb6 85.Re7 Bd8 86.Rg7 Bc7 87.Rg8+ Bb8 88.Rxb8#] 80.Rh3 Bg7 [ 80...Bc1 81.Kb6 Bb2 82.Rd3 Kc8 ( 82...Bf6 83.a7+ Ka8 84.Rd7 Bd4+ 85.Ka6!+- (85.Rxd4?? stalemate)) 83.Kc6 ( 83.a7 Bd4+ 84.Ka6 Bxa7 85.Kxa7+-) 83...Kb8 84.Rb3+ Ka7 85.Rxb2+-] 81.Rd3 denying the Bishop its d4 outpost for another three moves. [ 81.Rh7? Bd4= White can no longer put his King and Rook in contact with h7.] 81...Bf6 82.Rd7 Kc8 83.Rf7 Bd4 84.a7 Bxa7 85.Rxa7+-